Electrical Circuits

Electrical Circuits GEORG SIMON OHM (1789-1854) ALESSANDRO VOLTA (1745-1827) ANDRE MARIE AMPERE (1775-1836) RESISTANCE IN OHMS! POTENTIAL IN VOLTS! CURRENT IN AMPS!

Potential Difference (Voltage) Electric potential is average energy per charge. Energy is a relative quantity (absolute energy doesn’t exist), so the change in electric potential, called potential difference, is meaningful. A good analogy: potential is to temperature, as potential energy is to heat. Potential difference is often called voltage. Voltage is only dangerous when a lot of energy is transferred. SI Units click for web page Voltage & energy are scalars (no direction.) A volt (v) is the unit for voltage named in honor of Alessandro Volta, inventor of the first battery.

Sources of Voltage Voltage, also known as “electromotive force”, can be create by many sources of energy chemical hydroelectric nuclear solar wind geothermal biomass ALLESANDRO VOLTA AND THE ELECTRIC BATTERY A VOLTAGE SOURCE IS LIKE A WATER PUMP

voltage E field distance Potential Difference for Constant Electric Field Potential energy is often stored in a capacitor. Capacitors are made by putting an insulator in between two conductors. Most capacitors have constant electric fields. They store energy and are often used for quick discharge of energy like a flash for a camera. Example Calculate the magnitude of the electric field set up in a 2-millimeter wide capacitor connected to a 9-volt battery.

Electrical Current Current is the rate of flow of charge through a conductor. SI units Small microamp (μA) currents flow through your body, but larger amounts of current are dangerous, even deadly. Current flow is defined in the direction of positive charge; since electrons flow in wires, current is opposite the flow of electrons. ION FLOW IN A FLOURESCENT BULB

Electrical Current Potential difference creates an electric field which induces charge to flow in a circuit. Moving electrons collide with vibrating atoms, so they zigzag in a random path, with a slow drift velocity. click for animation The electric field travels at near the speed of light, but the drift velocity is less than a millimeter per second! Electrons do not race around a circuit. Electrons flow in solid wire circuits. Positive and negative ions flow in batteries (wet and dry cells), and in gas-filled light bulbs.

Electrical Resistance Resistance is a measurement of a material’s ability to resist the flow of electrical charge. ΔV SI units I R memory triangle Resistivity depends on the nature of a material. Conductors have low resistivity and insulators have high resistivity. Resistance depends on the material’s type, length, cross- section, and temperature. click for resistance codes resistance applet

Ohm’s Law Electrical circuit versus a water circuit click for animation click for animation When a device shows a linear relationship between voltage and current, it is said to be “ohmic” OHMIC NONOHMIC

Energy, Power, and Cost in Circuits POWER LAW Combine Power Law with Resistance equation (R = ΔV/I) Cost of Electrical Power Example - Find the cost of a 1500 watt hair dryer run for 12 minutes, using the rate of $0.16 per kilowatt hour. click for website

Kirchhoff’s Rules Rule #1 - The Loop Rule A statement of conservation of energy The sum of the potential differences (voltages) around any closed loop in a circuit must be zero Rule #2 - The Junction Rule A statement of conservation of charge The current entering a junction in a circuit equals the current leaving the junction

Series Circuits A series circuit has only one pathway around the circuit Rule # 1 means that the voltage across all resistors in series must add up to the source voltage ΔV1 ΔV2 ΔV3 ΔV Rule # 2 means that the current through all resistors in series must equal the source current Combine the two equations: click for animation

Parallel Circuits A parallel circuit has multiple pathways around the circuit Rule # 1 means that the voltage across all resistors in parallel must equal the source voltage ΔV1 ΔV2 ΔV3 ΔV Rule # 2 means that the current through all resistors in parallel must add up to the source current Combine the two equations: click for animation click for animation

Equivalent Resistance

Holiday Lights • Series wiring was often used for Christmas tree lights from 1900-1940 Most sets had 8 bulbs sharing 120 volts, so 15 volts each. But, when one bulb burns out they all go out! • Parallel wiring became popular in the 50s and 60s Each bulb has 120 volts and consumes ~10 watts (like a night light). When one bulb burns out, the rest stay on, but they use a lot of power - usually 250 watts per strand - and they get hot! Miniature lights became popular by the 1970s Most are 50 bulbs in a series “set”, then a few sets in parallel (up to 300), and use little power. To avoid “one out, all out” modern miniature bulbs use a “jumper” with insulation around it. When the bulb burns out, the jumper wire now has 120 volts across it, so the insulation burns off. The circuit is now complete. Now LED lights are popular and inexpensive Light emitting diodes (LED) use very little power, typically under 5 watts for 70 lights!

Applied Circuits Parallel circuits are used for wiring 120 volt outlets. Speakers in series or parallel • All devices plugged in get 120 volts • Each is independent of the others • As more devices are used, the total resistance decreases and total current increases. • Most circuits are limited to 20 amps. Batteries in series or parallel

Applied Circuits What type of wiring scheme is used for these circuits?

Combination Circuits click for animation click for animation A combination circuit must be simplified into groups of series and parallel resistors, and then the equivalent for each group is then found.

Combination Circuits The total current in the combination circuit is determined and used to work “backwards” to find other branch currents and resistor voltages. Find current through circuit Find voltage across 3Ω equivalent Find current through 12Ω equivalent Find voltage across 2Ω resistor

Electrical Circuits